SOLUTION: Why are there usually two solutions in quadratic equations?

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Question 35082: Why are there usually two solutions in quadratic equations?
Found 2 solutions by Prithwis, longjonsilver:
Answer by Prithwis(166) About Me  (Show Source):
You can put this solution on YOUR website!
They are the roots of the equation

Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
A solution is "where does the curve cross the x-axis".

A quadratic is a U- or a n-shape curve. Being such, this will cross the x-axis usually twice. sometimes never and occasionally just once, as shown in the 3 examples below:

One solution:
+graph%28300%2C300%2C-4%2C4%2C-2%2C20%2Cx%5E2%29+
Two solutions:
+graph%28300%2C300%2C-4%2C4%2C-6%2C12%2Cx%5E2-4%29+
No Solutions:
+graph%28300%2C300%2C-4%2C4%2C-2%2C22%2Cx%5E2%2B4%29+

jon.